If the ratio of sum of m terms and n terms of an A.P. is m2:n2, then the ratio of its mth and nth terms will be :
2m -1 : 2n - 1
m : n
2m + 1 : 2n + 1
2m - 2 : 2n - 2
SmSn = m2n2
= Smm2 - Snn2 = k(say)
TmTn = Sm−Sm−1Sn−Sn−1
= k[m2−(m−1)2]k[n2−(n−1)2]
= 2m−12n−1
If the ratio of sum of m terms and n terms of an A.P. is m2:n2, then the ratio of its mth and nth terms will be
If the ratio of the sum m terms and n terms of an A.P. are m2:n2 . Prove that the ratio of its mth and nth terms will be (2m-1):(2n-1).